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<A HREF="CAD_using_en.htm">See operating CAD manual</A>


<h2>Points</h2>

Points use the identification letter P.

See also: <a href="CAD_Base_en.htm#P">point codes</a>
See also: <a href="CAD_Base_en.htm#fmt_dynamic-obj">dynamic points</a>


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 <h2>PT cartes</h2>
Create point from cartesian coordinates.

   [BasePoint]          optional - <a href="CAD_input_en.htm#_PT_">BasePoint</a>
   [offset X-coord]     optional - set X-offset <a href="CAD_input_en.htm#_Val_">(value)</a>
   [offset Y-coord]     optional - set Y-offset
   [offset Z-coord]     optional - set Z-offset


  BasePoint:
   - key coordinates into field BasePoint (eg &quot;10,10,0&quot;)
   - or indicate position (left mouse button)
   - or select object; the point and the parametric value for the selected
       position is generated

  Relative:
   - select the base point and put the values for the offset distance
       into the fields "offset -"


 Example :
 Specifying an absolute 2D point.
   P1 = P(10 20) 
 Specifying an absolute 3D point.
   P2 = P(10 20 30) 
 Specifying a relative point (at a distance 10,10 from P2) 
   P3 = P2 X(10) Y(10) 



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  <h2>PT polar</h2>
 Create points from polar coordinates

   BasePoint       <a href="CAD_input_en.htm#_PT_">BasePoint</a>
   Angle-Rot.      rotate around the Z-axis of the active construction plane <a href="CAD_input_en.htm#_Angle_">(angle);</a>
   [Angle-Tilt]    rotate (tilt) normal to the Z-axis
   Dist.           distance from BasePoint


 Example:
 # P = BasePoint, RotationAngle, [Tilt Angle,] Distance 
 P5 = P4 ANG(90) 25 



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  <h2>PT rotate-Z</h2>
 Rotate a Point around the Z-axis of the active construction plane

   CenterPoint     rotate around this point an d the Z-axis
   Point/Vector    set point to be rotated (select point or vector)
   Angle-Rot.      rotate around the Z-axis of the active construction plane <a href="CAD_input_en.htm#_Angle_">(angle);</a>
   [Angle-Tilt]    rotate (tilt) normal to the Z-axis
   [Dist.]         distance from BasePoint


 Example:
 P3 = P1 P2 ANG(180) 
 # P2 is turned 180 degrees around P1.



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  <h2>PT rotate-axis</h2>
 Rotate a Point around a axis

   Point to rotate set point <a href="CAD_input_en.htm#_PT_">point</a> to be rotated 
   Rot-Axis        select <a href="CAD_input_en.htm#_LN_">line</a> as rotation-axis
   Angle           <a href="CAD_input_en.htm#_Angle_">angle</a> in degree


Example:
# P = point, rot-axis, angle
P21=P20 L20 ANG(30)    # rotate P20 30 degrees around line L20




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  <h2>PT translate</h2>
 Translate (move) point with a vector

   Point            point to move
   Direction-VEC    set direction/distance <a href="CAD_input_en.htm#_Vec_">(vector)</a>
   [Dist.]          length
   [Dist.Normal]    Distance - normal to "Direction" (in the construction plane)

P = BasePoint, Direction, [Distance,] [Normal Distance] 

Examples:
 # Translate point P1 with vector D1.
 D1 = 100 0 0 
 P2 = P1 D1 

 # Translate point P1 in the direction of the vector D1 at a distance of 12.
 P2 = P1 D1 12 





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  <h2>PT endpoints center focus ..</h2>
Get the characteristic point of an object.

   LN/CI/Curv    select curve
   Version       set which <a href="CAD_input_en.htm#_PTS_">type</a> of point


   PTS()     default        1         2          3           4 
  Line:    startpoint, startpoint, endpoint  midpoint.
  Circle:  centerpoint,startpoint, endpoint, centerpoint.
  Ellipse: centerpoint,startpoint, endpoint, centerpoint, focuspt-1, focuspt-2.
  Clothoid startpoint, startpoint, endpoint
  Plane:   origin.
  Model:   origin.


Beispiele:
P20=C20             # center of circle: or
P20=C20 PTS(1)
P24=L21 PTS(2)      # endpoint of line, or:
P24=P(L21 PTS(2))
P7=S20 PTS(2)       # endpoint of curve S20
P3=P1 P2            # midpoint
P3=L1 PTS(3)        # midpoint




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  <h2>PT control-points</h2>
Get control-points of a polygon or spline

   LN/CI/Curv    select polygon or spline
   point-Nr      set <a href="CAD_input_en.htm#_PTI_">point-number</a>

# get second point of polygon S20
P20=S20 PTI(2)




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  <h2>PT intersect  LN/CIR/CRV/PLN</h2>

 Create a point at the intersection of two objects

 # Intersection of a line with another line 
 P4 = L1 L2

 # Intersection a circle and a line 
 P5 = L1 C1 page

# Intersection of 2 circles 
P6 = C1 C2 side

# Intersection Line X Plane|RuledSurface
P6=L10 R20
P6=INT L10 R20



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  <h2>PT Proj. PT -> LN/CIR/CRV/PLN</h2>
Project a point perpendicular onto an object.
  Object: line,circle,polgon,ellipsis,b-spline,plane
  Version: (1-n, PageUp/dwn-key)

 # Project Point onto Line:
 P2 = P1, L1
 # Line defined by Point + Vector:
 P3=P2 P1 DX
 # projects P2 onto Line P1-DX (horizontal, unlimited, through P1)

 # project Point onto circle
 # The standard solution is the nearer point.
 P7 = P1 C1 MOD(2) 
   MOD(2) defines the distant point.

 # Projection of the point P10 to the plane R1.
 P11 = P10 R1 

 # Point on curve project.
 P11 = P1 S10 MOD(1) 
   P1-P11 now form a normal to S10 at point P11.
   MOD (1) =-first solution.


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  <h2>PT Proj. PT along VC -> PLN</h2>
 Projects a point along a vector onto a plane. 

Example:
R20=P(50 0 0) D(1 0 1)
D20=D(1 0 1)
P28=P(10 0 0) D20 R20
  


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<p><a name="F7"></a></p>
  <h2>PT parametric on LN/CIR/CRV/SUR</h2>
Create a point on Line / Circle / Curve / Surface using parameter/s.

   LN/CI/Curv/Surf        select line, cirle or curve (*1)
   Parameter along        key parameter (*2)
   [Parameter across]


(*2)  Parameters field is 0 to 1; 0.5 defines the middle.

(*1) Surfaces (RuledSurface, RevolvedSurface or B-SplineSurface):
     Two parameters are required (U and V), along and across the direction.
     Not all types of surfaces supported yet.


Example:
# midpoint of line:
P23 = L20 VAL(.5)

# Point on surface, U-value, V-value; range is 0 - 1 !
P1=A1 0.5 0.5
# or
P1=A1 VAL(0.5) VAL(0.5)



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